Chemical analysis using neutrons



Sept. 4, 1951 K. c. CRUMRINE CHEMICAL ANALYSIS usms NEUTRONS 2Sheets-Sheet 1 Filed Aug. 2, 1948 FIG. I.

DETECTOR CYLINDER d =ICMr sd IO CM KMWKW v A E Y n C ww R m m. T. TV m3SA M w m E m mm NFG AC .0 N0 MF El FmRm m EEO NBC I I I MASS I VELOCITYMASS VELOCITY ATTORNEY Sept. 4, 1951 K. c. CRUMRINE CHEMICAL ANALYSISUSING NEUTRONS 2 Sheets-Sheet 2 Filed Aug. 2, 1948 MUQDQM m mik u no?INVENTOR. KENNETH C. CRUMR/NE A TTORNE Y Patented Sept. 4, 1951 CHEMICALANALYSIS USING NEUTRONS Kenneth C. Crumrine, Tulsa, Okla., assignor toThe Texas Company, New York, N. Y., a corporatlon'of DelawareApplication August 2, 1948, Serial N 0. 41,962

'2 Claims. 1

This invention relates to chemical analysis and particularly to theanalysis of mixtures of carbonhydrogen compounds and other compoundscontaining hydrogen or other elements of large interactioncross-sections for neutrons. The invention is particularly applicable inoil refineries, where it affords a simple and reliable means fordetecting changes in the composition of a hydrocarbon mixture in a pipeor a vessel, say a still.

Neutrons are produced in several ways. A convenient way is to bombardberyllium with alpha particles, the neutrons being formed as the resultof the reaction where m represents the neutron and indicates that it haszero charge and unity mass number. The alpha particles may come fromvarious sources. for example radium or radon, and a conventional sourceof fast neutrons consists of a mixture of radium and beryllium.

In accordance with the instant invention a. material to be analyzed issubjected to neutron bombardment, and the analysis of the material isdetermined by detecting the neutrons transmitted through the material orback-scattered from it. Hydrogen and some other elements have relativelylarge cross-sections for interaction with neutrons. In consequence, themean free paths of neutrons in carbon-hydrogen compounds vary, dependingupon the ratio of carbon to hydrogen in the compounds. By way ofexample, the mean free paths of slow neutrons in C4H2, CiHi, C4Ha, C4Hs,and C4Hro are respectively about 1.6 cm., 0.81 cm., 0.60 cm., 0.48 cm.,and 0.44 cm. The neutron mean free paths in members of the same familyof carbon-hydrogen compounds show smaller differences. For example, inthe CiHa group, butadiene (CHzzCI-ICHzCI-Iz) and l-butyne (CHzCCHzCHa)have mean free paths in the inverse ratio of their densities, or say as.612 is to .596. Mixtures of compounds have mean free paths dependentupon the neutron mean free paths of the individual components. Thus abinary mixture of Cid-la and C4H1o will have a mean free path forneutrons intermediate 0.60 and 0.44 cm.

The transmission and scattering of neutrons depend upon the mean freepath in the medium in which the transmission and scattering occurs.Scattering may be considered as transmission through at least a portionof the body. Hence the measure of transmission or scattering or both isa measure of mean free path and consequently an index of the compositionof the medium. To take a simple case of the practice of the invention, aliquid mixture of Gil-Is and C4Hw is passed as a stream through a steelpipe. A source or fast neutrons, say a mixture of radium and beryllium,is placed on one side of the pipe. Neutrons pass through the steel ofthe pipe and are slowed down chiefly by the hydrogen content of themixture. Some of the neutrons are backscattered toward the source;others are transmitted through the mixture. A neutron counter isdisposed outside the pipe in the path of the backscattered or of thetransmitted neutrons, and the number of neutrons per unit time isdetected. The number detected per unit time (intensity) for a givensource, detector and geometry is a function of the neutron mean freepath in the mixture and hence of its composition. By making a continuousrecord of detected neutron intensity, a continuous index of theproportions of 041-16 and C4H10 in the mixture passing through the pipeis obtained.

Neutron source, material to be analyzed, and detector should be disposedin a fixed geometric relationship, and a standard thickness of materialshould be employed. In practice, this latter requisite is met by keepingthe material in a vessel of fixed dimensions such as a pipe or a tank.

As noted at the outset, there are numerous satisfactory artificialneutron sources for use in the invention. The bombardment of berylliumwith alpha particles to produce neutrons is but one of a number of a-TLreactions. Thus alpha bombardment of lithium, boron, sodium, magnesium,aluminum and phosphorus also results in neutron production. Thebombardment of heavy hydrogen by deuterons also results in neutronemission.

The neutrons employed in the practice of the invention may be emitted inall directions or may be collimated in a beam employing a neutronhowitzer, for example that described by Powers, Carroll and Dunning,Phys. Rev., vol. 56, p. 266 (1938).

It is shown in the detailed discussion which follows that increaseddiscrimination between compounds in the practice of the invention isobtained if the neutrons employed to bombard the mixture (in which thecompounds occur) do not have excessive energy. By selecting a propersource and employing filters or screen to absorb those neutrons havingan energy below a desired threshold value, say 1 ev., neutrons in anydesired energy range or spectrum portion may be obtained. Thus a cadmiumscreen may be interposed between the neutron and the material undergoinganalysis to absorb thermal neutrons, etc.

Various types of neutron detectors may be employed. One suitable form isa proportional counter lined with boron carbide and sensitive to slowneutrons. Fast neutrons from the source pass through the walls of thevessel, are slowed down by collision with hydrogen nuclei and are eitherscattered back or continue through the mixture at reduced energy. Theneutrons that have their energy reduced, whether they be backscatteredor continue through the mixture, are susceptible of detection by thecounter, while the fast neutrons are not detected.

The proportional counter lined with boron carbide is only one of anumber of devices available for the detection of slow (low energy)neutrons. Gaseous boron trifiuoride may be employed as filling tosensitize a proportional counter to slow neutrons, and either solid orgaseous lithium compounds may be employed to the same end. A counterlined with uranium and operating by fission may also be employed for thedetection of slow neutrons.

Counters for fast neutrons are also available. Thus an ionizationchamber filled with hydrogen at high pressure is effective in detectionof fast neutrons. Proportional counters for slow neutrons may also beemployed by protecting them with shields of hydrogen-containingsubstances which serve to slow neutrons to a detectable range.

It is within the contemplation of the invention to detect the intensityof either fast or slow neutrons emitted from the sample undergoinginvestigation and to measure the intensity of only those emittedneutrons in a given energy range.

The invention offers the advantages of rapid and continuous analysis,and is particularly use ful as a method of control for refineryoperations or the like. Generally speaking, its usefulness is less whenthe numb-er of carbon-hydrogen compounds in a stream is large, or whenthe compounds do not have markedly different mean free paths, since inthese cases the discriminatory power of the process of the invention isdiminished. Nevertheless, there are a great many places in oilrefineries and chemical plants where the invention is applicable notonly to continuous quantitative analysis of mixture streams, but also toautomatic process control through electrical or mechanical linkageswhich operate a control means, say a valve, in response to variations indetected neutron intensity.

The invention will be more thoroughly understood through reference tothe following discussion which is illustrated by the accompanyingdrawings, in which:

Fig. 1 is a diagram illustrating the geometry assumed in the derivationof a number of working equations set forth below;

Fig. 2 is a diagram illustrating neutron and nucleus before and aftercollision in a C. G. sys- Fig. 3 is a diagram illustrating scatteredneutron velocity as a vector sum;

Fig. 4 is a plot of the fractional transmission of neutrons at variousenergies through various hydrocarbons employing apparatus of thegeometry of Fig. l; and

Fig. 5 is a diagram illustrating another geometrical arrangement for thepractice of the invention.

Referring to Fig. 1, a main stream of a hydrocarbon mixture to beanalyzed is shown as flowing in a pipe. A sample or side stream istapped off the main stream and flown through a scatt rer cylinder Shaving a diameter d. of 2 cm. and a thickness X, the cross-section areaof the cylinder being A=1r cm.. A detector D for neutrons is disposedcoaxially with the scatterer cylinder with its face a distance w1=10 cm.from the center line of the scatterer. The detector has a diameter d=1cm. so that its face area Ad=1I'/4 cm.". A point source Q of neutrons isdisposed on the common axis of detector and scatterer at a distance ofw=10 cm. from the center line of the scatterer and opposite thedetector. The scatterer has a wall of some material of low scatteringcross section, such as magnesium or aluminum.

A set of working equations has been derived for the geometry of Fig. 1,as follows:

I. Tmmsmssron BY Pom-r SCATTERER 'ro Pom Dsrncron When a neutron beamtraverses an element of volume AXAYAZ in the X direction, the number ofneutrons in the beam is reduced by the action of scattering from thenuclei in the volume element:

AN=-FNAX where F has the meaning "the fraction of neutrons scattered outper unit distance, and has dimensions, cm.

To express F in terms of measurable quantities, it appears from itsdefinition above that F (nuclear area/total area) per unit distance (nnuclei/cm. X

(AX AYAZ 0111.) X S (emf/nucleus) l (AYAZ cm?) AX cm.

If the above equation for the attenuation of the beam is expressed indiiferential form and integrated it yields and the transmission TEN/No='e- =e For a scatterer with nuclei of more than one type ns thefollowing summation must be used:

where To deal with hydrocarbons only, the relevant special case ofEquation 1 is T =e (nusu-i-ncsco X (1A) II. CORRECTIONS FOR (A) FmzrnSCATTERER AND DETECTOR; (B) PREFERENTIAL FORWARD ScA'rmama curved arearepresents a. good approximation for the case of small solid angles.)

51 Now the number that are single-scattered into D by the nuclei in Scan be calculated thus:

Therefore, calling 1' the corrected transmission,

which, for the special case vqs=wsd==m becomes Act/4178i to obtain thenumber scattered into D. This correction is right provided neutrons arescattered with equal probability in all directions. To keep the analysissimple, such isotropic scattering by the nucleus is assumed, and yet itis isotropic only in the coordinate system of the center of gravity. Fora very heavy nucleus the C. G. system would practically coincide withthe laboratory system and isotropiescattering could be assumed in bothsystems. For hydrogen the neutron and nuclear masses are equal, and theC. G. system is moving with half the speed of the incident neutron. Inthis case the scattering, which is isotropic in the C. G. system, isbunched forward in the laboratory system.

This latter effect occurs only when the struck nucleus is free torecoil. In the hydrocarbons binding energies are of the order of anelectron volt. Therefore the efiect discussed above is considered asreal for neutrons above 1 ev., where the nucleus will be rendered freeto recoil, and as not real for neutrons below 1 ev., when the strucknucleus stays bound to the molecule and acts as though it had the massof the whole molecule (effectively infinite).

If E is the angle which upon rotation generates the cone with altitude78d and base area As, then the solid angle of the cone is (l-cos E) [2.Now the effect of preferential forward scattering is to drive moreneutrons into D than correspond to the angle E and the solid angle(l-cos E) /2; the correct number of neutrons will correspond to somelarger angle E and solid angle (1-cos E )/2. The correction factor thatis to be multiplied by Ari/4mm then will be (l-cos E )/(1cos E). Toobtain the relation between E and E consider the following:

If a neutron, with velocity in and mass 1, approaches a nucleus whosevelocity is zero and mass is M, the C. G. system is moving with velocity(1/M+1)'m in the laboratory system. The velocities in the C. G. systemthen are represented as shown in Fig. 2. The velocity in the C. G.system of each particle in an elastic scattering collision changes indirection but not in magnitude.

To obtain the velocity, v, or the direction, E, 01' the scatteredneutron in the laboratory systom, the neutron velocity in the C. Gsystem must be added vectorially to the velocity of the C. G. system inthe laboratory system as shown in Fig. 3. From this vector diagram it isseen that Therefore the correction factor to be applied to Ari/mad isCos E= 1 cos E 1 cos E lcosE McosE +1 /M+1+2M cos E In the assumedgeometry E=0.05 radians, and the corrections calculated with Equations 3and 4 are:

4.9 for M==1 (hydrogen nucleus) 1.2 for M 12 (carbon nucleus) Thereforein place of rid/4 m the correct term is Ad 41 st! (4.0x the fractionscattered by H+ 1.2x the fraction scattered by C) or Ad 4.0n s +l.2n s

41ryl3d n38 +nc C and Equation 2A is replaced by A1 4.0n1;8 1.21ZC8C 1 niric c for neutron energieszl ev. and remains unmodifled for neutronenergies l ev.

Now putting in the values from the assumed geometry, Fig. 1, via:

0.040n s +0.012nsc h nsa -l-nsuc)] (6) nn a-i-nc c for neutron energieslev. and

for neutron energies 1 ev. where T is the fractional transmission toneutrons of a certain energy no. neutrons of that energy arriving at D,

Fig. l with S in the beam no. neutrons of that energy arriving at D withS out of the bee.

nu is the number of H atoms per cm. in S no is the number of C atoms percm. in 8 SH is the cm. cross section of H for neutrons of the energyconsidered so is the cm. cross section of C for neutrons of the energyconsidered Mower-Equation 6A is not entirely accurate, especially at thelower (thermal) energies of its range. A number of eifects take placewhich tend to mask the simple effects considered above. These low energyeffects include: multiple scattering, more likely at the high crosssections: chemical bond effect; molecular motion eifect; neutron captureby impurities; non-isotropic scattering,

III. EQUATIONS roe CALCULATING where A is Avogadros number, 0.603molecules/mole; d is density of the hydrocarbon sample in gm./cm. "Jim.and um are the number of H-atoms and the number of C-atoms per molecule.

M is the molecule weight of the hydrocarbon sample in gm./mole.

If R=TLHm/Tl-Cm, and

(which is practically a constant for all heavy hydrocarbons) M ah, theequation 7 becomes T=0.040+o.9soe" (s) for neutrons of energies l ev.and

T=0.o1o+0.990e' (8A) for neutrons of energies 1 ev.

An expression for the change in transmission as a function of change incomposition of the sample is desirable. Since SH and so are constant andk is practically constant over a variation in composition, an expressionfor the change of T with a change of R and d can be obtained bydifierentiatlng Equation 8. Since in Equation 8 the so term is smallcompared to the Rsg term in the exponent, little error is introduced byholding the density constant at some value ch in this term during thedifferentiation.

kd 1a %=ks A(Rd) [l-0.042e which, upon numerical evaluation in the rangeof energies for which Equation 8 is valid, is found to be wellapproximated by ks A (Rd) for neutron energieszl ev.

Similarly, starting with Equation 8A it can be shown that and (10) wherennmi and ncmi are the numbers of H and C atoms per molecule 01' typeiand X1 and iii are the mole fraction and density of compound of type 1'.

However for binary mixtures a good approximation is where R1 and R2 arethe H to C ratios in pure compounds 1 and 2, and di and d: are thedensities of pure compounds 1 and 2.

IV. SAMPLE CALCULATIONS To summarize the working equations, which applyonly to the geometry shown in Fig. 1; the exact transmission equationsare:

0.040n s +0.0.2n s (1I, a +n a ns a+ne e [1 e l (6) for neutron energies1 ev.

T=0.01o+0.990@""" (6A) for neutron energies 1 ev.

Approximate transmission equations:

T=0.O40+0.96Oe' d(Re -Fa (8) for neutron energies 2 1 ev.

T=0.010+0.990e' %d(Rs -l-s (8A) for neutron energies 1 ev.

Fractional change in transmission:

ATIT=A%sHA(Rd) (9) for neutron energies 2 l ev.

ATIT= A s A(Rd)[19.010e+A%d(Rs +s for neutron energ1es 1 ev. where, tocalculate (Rd) the terms employed are R i Hni i CIH' I' (10) d= E dX; I

or the approximation which is suitable for small changes in binarymixtures,

A(Rd)=-AX (Rah-Ruiz) (11) GLOSSARY A=0.603 x 10" molecules/ mole.

ncm=no. C-atoms per molecule (or effective no.

per molecule if a mixture).

M=molecular weight of sample (or effective molecular weight if amixture) gm./mole.

d=density of sample (or effective density if a mixture) gm./cm.

d1=density of compound of type i.

R=ratio of H-atoms to C-atoms in sample.

an and sc=cross sections of H- and C-atoms for neutrons of energy beingconsidered.

ns and ne=no. of H- and C-atoms per cmfi.

mum and nomi=no. H- and C-atoms per molecule oitypei.

Xi=mo1e traction oi compound or type i.

assess:

For sample calculations the following hydrocer eons mu be used:

The graph (Fig. 4) shows a plot 01 I' for of these hydrocarbons over a.range 015 10 to 10" ctr. of neutron energies. Values for sections usedare the total cross sections? for H and C published by Goldsmith, Ibser,and Feld in both Rev. Mod. Phys. 19, 259 (1947 and IheScience andEngineering of Nuclear Power Seminar Notes), p. 393, vol. 1, edited byC. Goodman. Addison-Wesley Press, Cambridge. Mass. (1947). This graph isnot intended to be accurate throughout, but rather to indicate roughlythe amount of transmission to be expected at the various energies. Eachcurve is simply a series of straight lines connecting the pointscalculated at energies 10 10 1, 10, 10*, 10, 10", and 10" ev. Thecalculations were made using the exact Equations 6 and 6A.

The satisfactory character of the approximation in Equation 8 is shownby the comparison table A which follows: Equation 6A and 8A areidentical.

l0 se=4.l for case (it); 45x10- for case (b); 2.4x10- for case (0)d=0.614 R=2.4

Calculation (a) 4.3% by Eq. 9A

ATIT= -A%SHA (Rd) =4.s%

by Eq. (9), not valid for this low energy.

Calculation (b) AT/T=2.8% by Equation 9A AT/T=3.0% by Equation 9Calculation (c) AT/T=0.6% by Equation 9A AT/T=0.6% by Equation 9 SAMPLECALCULATION 2 Problem A mixture of n-butane and Z-butyne changes itsn-butane concentration from 60% to 70%. What is the percent change inneutron transmission at 10 ev.?

Outline First calculate MRd) from Eq. 11. Then calculate AT/ T from Eq.9.

TABLE Neutron n-Butane lsobutyiene 2-Butyne g? Xmmem" Xmiiem" Exact, Apron, Eqact, A pron, Exact Approx., 7 E11. (0 E q. (s) V Eq. 0 1.1.(8)10 05 Eq. (s)

11 15 as 0.020 0. 020 0.044 10- s 4.1 7 0.101 0. 110 0. 112

1 22 4.5 0. 204 0. 250 0.270 0.211 0.342 0.344 10 21 V 4.4 0. s 0. 2100.200 0.202 0. 354 0. s57 10 I 10. s 4. s 0. 289 0. 292 0. 310 0. 01s 0.37s 0. s10 10 1 1s 4. a 0. 411 o. 410 0. 130 0. 43a 0. 495 0. s 10. 4.52.4 0.122 0.124 0.120 0. 731 0.101 0.700 10 1 0.8 1. 0. 034 0.035 0.0130 0.020 0. 034 0. 935

SAMPLE CALCULATION 1 Data Problem Ax=.10 A mixture of n-butane andisobutylene changes Effits n-butane concentration from 20% to 40%. 1: 5'What is the percent change in neutron transmission at A=0.603X10' (a)10- em? i=4. (0) 1W? M=55. (c) 10 ev? sn==19.5 For a measure of errorcaused by using wrong c l t e uation, cal late e h c both 9 d M. by anA(Rd) =AX(R1d1Rzd1) =.o47 by Eq. 11

n AT T=A %sEA(Rd =4.0% by Eq. 0 First calculate A(Rd) from Eq. 11. Thencalculate from Eq- 9, also from Eq- QA- 3 Data 05 l Ax=20 Prob cm R1=2.5V A ternary mixture of n-butane, isobutylene, R2=2.0 aim 2- butyne inthe proportions %30-10 d1=0.60 changes to the proportions 50-20-30. Whatis dz=0.6'l the percent change in neutron transmission at A=0.603X10 10ev.? M==57.6 nem=4 Outline sn=36 10-" for case (a); 221x10 for case (b);4.5x10- for case (0) first calculate MR6) frorn Ed. 10. ThencaloulatenT/T from Eq. 9.

Data

2.10 by Eq.

It has been demonstrated that (1) A change in composition of a mixtureof n-butane and isobutylene from -80 proportions to -60 proportions isaccompanied by a percentage change in neutron transmission of 4%, 3% and0.6% at neutron energies respectively of 10 ev., 1 ev., and 10 ev.;

(2) A change in composition of a mixture of n-butane and 2-butyne from-40 proportions to -30 proportions is accompanied by a change in neutrontransmission of 4% to 10 ev.;

l3) A mixture ofn-butane, isobutylene and Z-butyne which changes from60-30-10 proportions to 50-20-30 proportions will cause a change inneutron transmission of 1.5% at 10 ev.

Such examples may be multiplied indefinitely, employing the generalizedequations which have been developed. The three sample calculations donot, by any means, express maximum changes in neutron transmission, forwith mixtures of hydrocarbons having greatly different hydrogencontents, the change in transmission with change in proportion ofconstituents will be even more marked.

It has been observed that the maximum percent changes in neutrontransmission occur at low neutron energies, although the maximumabsolute changes are in the range of l ev. to 10 ev. Even bearing inmind that the calculations for energies below 1 ev. cannot be consideredas extremely accurate, it is apparent that in the practice of theinvention, increased discrimination between compounds in a mixture is tobe obtained with neutron energies of not to exceed 10 ev.

The calibration of apparatus employed in the invention is simple. Theneutron source, the vessel for the samples, and the detector aredisposed in a desired fixed geometrical relationship,

12 say that illustrated in Fig. 1, and intensity readings are takenwhile the vessel is filled with each of a series of samples. Incalibrating for a given binary mixture, for example, intensity readingsare taken for the individual components and for mixtures containingvarious proportions of the two components. Intensities are then plottedagainst proportions to produce a curve which shows at a glance theintensity representative of particular proportions in the mixture.

The invention may be employed to compare succeeding portions of astream, as already described, or it may be employed to compare batches,say binary mixtures containing the same components but in differentproportions. In either case intensity readings are obtained forsucceeding portions or different batches, preferably employing the samegeometrical relationship of source, sample and detector in each case.

Although the invention has been described with reference to a particulargeometric arrangement, it should be understood that measurement of theintensity of scattered, as distinguished from transmitted neutrons, alsopermits determination of change in composition. This is illustrated inFig. 5, wherein the detector is placed at an angle with respect to thebeam of neutrons. The practice with the apparatus of Fig. 5 is the sameas with the apparatus of Fig. 1. Neutron intensity, in terms of countsper unit time, is observed continuously at the detector. and is an indexof changing composition in the hydrocarbon stream which acts to scatterthe neutrons and reduce their energy.

The process of the invention is applicable to the analysis of solid,gaseous, and liquid mixtures, but finds its greatest application incontinuous analysis of liquid and gaseous streams in oil refineries andthe like. All that is required for the practice of the invention is aneutron source, a sample in a vassel or conduit, a neutron detector, andconventional amplification and recording equipment employed with suchdetectors. Any geometric arrangement may be employed which permitsneutrons from the source to penetrate the sample and be transmitted orscattered to the detector, a fixed geometry being preferable because ofthe simplicity it lends to comparative analysis.

I claim:

1. In the analysis of a mixture of carbonhydrogen compounds, theimprovement which comprises bombarding a fixed fluid cross section ofthe mixture with neutrons having an energy not to exceed 10 ev.,determining the intensity of neutrons emerging from the mixture andcomparing this intensity with a neutron intensity determined bybombarding a fixed fluid cross section of known composition andcontaining a carbon-hydrogen compound with neutrons having an energy notto exceed 10 ev. and determining the intensity of neutrons emerging fromthis second cross section.

2. In the analysis of a mixture of carbonhydrogen compounds, theimprovement which comprises bombarding a fixed fluid cross section ofthe mixture with neutrons having energies in the range of about i toabout 10 ev., determining the intensity of neutrons emitted from themixture and comparing this intensity with a neutron intensity determinedby bombarding a second fixed fluid cross section of known compositionand containing a carbon-hydrogen compound with neutrons having energiesin said 13 range and determining the intensity of neutrons emitted fromthe second cross section.

KENNETH C. CRUMRINE.

REFERENCES CITED The following references are of record in the file ofthis patent:

Number 14 UNITED STATES PATENTS Name Date Brons Nov. 5, 1940 Hare Dec.15, 1942 Hare Apr. 13, 1943 Brunner Mar. 16, 1948 Lipson Feb. 22, 1949Friedman et a1. Nov. 15, 1949 Certificate of Correction Patent No.2,567,057 September 4, 1951 KENNETH C. CRUMRINE It is hereby certifiedthat error appears in the printed specification of the above numberedpatent requirmg correction as follows:

Column 4, line 57 Equation (1A), strike out and insert therefor aclosing parenthesis; column 5, line 13, strike out 803*, secondoccurrence; column 6, line 7 before 1r insert 4; column 7, line 25, for5k read =11; line 65, for A(9) read (9A); column 8, line 45, for thatportion of the equation reading 1 9.010e+ read 1 0.010e+ line 54, for d,second occurrence, read d column 11, line 25, in the denominator in thefirst equation, for n reed n and that the said Letters Patent should beread as corrected above, so that the same may conform to the record ofthe case in the Patent Oflice.

Signed and sealed this 29th day of January, A. D. 1952.

THOMAS F. MURPHY,

Amlatant Oommissioner of Pat ents.

1. IN THE ANALYSIS OF A MIXTURE OF CARBONHYDROGEN COMPOUNDS, THEIMPROVEMENT WHICH COMPRISES BOMBARDING A FIXED FLUID CROSS SECTION OFTHE MIXTURE WITH NEUTRONS HAVING AN ENERGY NOT TO EXCEED 104 EV.,DETERMINING THE INTENSITY OF NEUTRONS EMERGING FROM THE MIXTURE ANDCOMPARING THIS INTENSITY WITH A NEUTRON INTENSITY DETERMINED BYBOMBARDING A FIXED FLUID CROSS SECTION OF KNOWN COMPOSITION ANDCONTAINING A CARBON-HYDROGEN COMPOUND WITH NEUTRONS HAVING AN ENERGY NOTTO EXCEED 104 EV. AND DETERMINING THE INTENSITY OF NEUTRONS EMERGINGFROM THIS SECOND CROSS SECTION.